Construct the Perpendicular Line Through a Given Point on a Line (GeoGebra)

This example demonstrates how to construct the perpendicular line through a specified point located on a given line. Using the circle–intersection method, students locate auxiliary intersection points that create equal radii, enabling the derivation of a right angle with clear geometric reasoning. Key math concepts include perpendicularity, circle constructions, congruence/equal-distance arguments (often framed via isosceles triangle or equal radii), and angle relationships. In GeoGebra, the construction relies on Point to create key points, Line to represent the original and constructed lines, Distance to set the circle radius from known segments, Circle to draw the construction circles, and Intersect to compute circle-line/circle-circle intersection points that guide the final perpendicular. The activity also supports interactive steps (e.g., sliders and navigation controls) for comparing procedures with and without GeoGebra, making it suitable for middle-school geometry lessons, practice with classical constructions, and exploratory learning.